Steam+Linux - Would I need to buy one or two copies?

[pxc]

Hmm...

With the purchase completed, I have an order number (which I use to download from FG) and a serial number. Using the serial number as the input for Steam's "Activate a Game on Steam" function fails, reporting an invalid key.

Meanwhile, I'm downloading the versions of the game that I need, and I can later set up a shortcut within Steam to run these games independently.

Still, since Steam offers the game for sale alongside FG, it would be nice to be able to register my FG copy on Steam for automatic updates, etc.